Home
Class 12
MATHS
A curve passes through the point (1,(pi)...

A curve passes through the point `(1,(pi)/(6)).` Let the slope of the curve at each point (x,y) be `(y)/(x)+sec((y)/(x)),xgt0.` Then, the equation of the curve is

A

`sin((y)/(x))=logx+(1)/(2)`

B

`cosec(y)/(x)=logx+2`

C

`sec((2y)/(x))=logx+2`

D

`cos((2y)/(x))=logx+(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Differential Equations Exerise 7 :|1 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

Find the equation of a curve passing through the point (1,pi/4) if the slope of the tangent to the curve at any point P(x,y) is y/x-cos^2(y/x)

Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is (y-1)/(x^2+x) .

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the equation of a curve passing through the origin if the slope of the tangent to the curve at any point (x,y) is equal to the square of the difference of the abscissa and the ordinate of the point.

Find the equation of a curve passing through (2,1) if the slope of the tangent to the curve at any point (x,y) is (x^2+y^2)/(2xy)

Find the equation of a curve passing through the point (–2, 3), given that the slope of the tangent to the curve at any point (x, y) is 2x/y^2

Find the equation of a curve passing through the point (1.1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (– 4, –3). Find the equation of the curve given that it passes through (–2, 1).

Find the equation of a curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Solve the differential equation : y sqrt(1-x^2)dy-sqrt(1+y^2)dx=0

    Text Solution

    |

  2. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  3. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

    Text Solution

    |

  4. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  5. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

    Text Solution

    |

  6. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  7. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |

  8. Differentiate the following w.r.t x (log x)^(cos x)

    Text Solution

    |

  9. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  10. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

    Text Solution

    |

  11. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

    Text Solution

    |

  12. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

    Text Solution

    |

  13. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

    Text Solution

    |

  14. Let the population of rabbits surviving at a time t be governed by t...

    Text Solution

    |

  15. At present, a firm is manufacturing 2000 items. It is estimated tha...

    Text Solution

    |

  16. The population p(t) at time t of a certain mouse species satisfies the...

    Text Solution

    |

  17. If (dy)/(dx)=y+3 and y(0)=2, then y(log2) is equal to

    Text Solution

    |

  18. Let I be the purchase value of an equipment and V(t) be the value afte...

    Text Solution

    |

  19. Solution of the differential equation cosxdy=y(sinx-y)dx, 0ltxlt(pi)...

    Text Solution

    |

  20. The differential equation which represents the family of curves y=c(1)...

    Text Solution

    |